Predictive equations of normalized shear modulus (G/Gmax) and material damping ratio (D) are presented for calcareous sand, siliceous carbonate sand and carbonate sand of the Bay of Campeche and Tabasco Coastline. This was achieved using a database of 84 resonant column tests and 252 strain-controlled cyclic direct simple shear test that provide data to define the normalized shear modulus, G/Gmax, and material damping ratio, D, versus cyclic shear strain. The range of cyclic shear strains of the database is from 0.0001% to 1%, and the range of carbonate content (Ca2CO3) from 10% to 100%. The curves of normalized modulus reduction and damping ratio were organized in three groups according to the percentage of carbonate content: 1) calcareous sands (10% to 50%), 2) siliceous carbonate sand (50% to 90%) and 3) carbonate sands (90% to 100%). Two independent modified hyperbolic relations for normalized modulus reduction and material damping ratio versus cyclic shear strain were developed for each group. The normalized shear modulus was modeled using two parameters: 1) a reference strain defined as the strain at which G/Gmax is equal to 0.5, and 2) a parameter that controls the curvature of the normalized modulus reduction curve. The material damping ratio was modeled using four parameters: 1) a reference strain γrD defined as the strain at which D/Dmax= 0.5, 2) a curvature parameter αD that controls the curvature of the material damping ratio curve, 3) a maximum material damping ratio Dmax, and 4) a minimum material damping ratio Dmin. The new empirical relationships to predict the normalized modulus reduction and material damping ratio curves as a function of effective confining pressure are easy to apply in practice and can be used when site-specific dynamic laboratory testing is not available. The curves of G/Gmax-γ and D-γ, are similar between silica sand and calcareous sand. The curves of siliceous carbonate sand and carbonate sand are very similar, but show a different shape and width than the curves of silica sand and calcareous sand. This indicates that when the carbonate content is smaller than 50% there is a small effect on the curves of G/Gmax-γ and D-γ, and a considerable effect when the carbonate content is greater than 50%.